1. What, if any, connections do you see between learning and computer/video game playing?
All games are fundamentally about learning, more than anything else. I think that good games are designed to give the player a satisfying learning experience -- right amount of challenge, variation, etc...
2. What connection, if any, do you see between computer games and the teaching of writing at either the high school or college level?
This is probably a connection to be made. There are certainly many aspects of video games that can be analyzed using English tools. Some game types, especially adventure games, are good examples of what text can do -- i.e. create interesting worlds by simply describing them.
3. What do you suppose might be an interesting computer game for the teaching of writing (either currently out or not yet imagined)?
Since computer don't really appreciate writing, I would think it has to be a game where the core experience is about writing something that is then evaluated in some form by other players/users. This would give users a sense of writing as communication as well.